### Brain Teasers

# Cats and Mice

A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. How many cats do you think there were?

There are two conditions:

a) It is not one cat that killed the lot because I have used the word 'Cats'

b) It is not 999919 cats because I have used the word 'mice'.

There are two conditions:

a) It is not one cat that killed the lot because I have used the word 'Cats'

b) It is not 999919 cats because I have used the word 'mice'.

### Answer

The number 999919 cannot be a prime number at first glance. If the problem has only one solution, then this number should have only 2 factors. The factors are 991 and 1009 which are both prime. Since each cat killed more mice than there were cats the answer is clearly that 991 cats killed 1009 mice.Hide Answer Show Answer

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## Comments

I like this kind of teaser. I got the factors easily enough. However, both solutions should be allowed. At no time does the teaser indicate that there were fewer cats than mice.

The teaser is good but Gizzer is right.

The teaser did not indicate the number of cats was lower than the number of mice.But very good teaser, anyway.

The teaser did not indicate the number of cats was lower than the number of mice.But very good teaser, anyway.

I agree about two answers. I loved the puzzle. Arriving at the factors is interesting. You could use a spreadsheet I suppose. Or writing 999919 as 1000000-81 it is recognisable as the difference of two squares; namely 1000^2 - 9^2. This can be factorised into the product of their sum and difference. That is (100+9)(1000-9). Thus the two factors are 1009 and 991. There is nothing in the puzzle to suggest that the number of cats could not be either. So 1009 cat killed 991 mice each or 991 cats killed 1009 mice each. Either way, that's a lot of tired pussies!

oops! That should be (1000+9)(1000-9). Hehe..typo!

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